To understand a protein's function and to design new proteins with new functions, it is essential to know the physical principles that control the structure, folding, stability, and dynamics of protein molecules. Our long-term research interest is to investigate these principles and use them to solve practical problems in basic medical research and development of protein drugs. Currently, we are studying the mechanism of protein folding using various tools including stopped-flow spectroscopy, NMR, hydrogen exchange, protein engineering and phage-display.In the past several years, we focused on studying the folding mechanism of small proteins including cytochrome C (104 amino acids), Rd-apocyt b562 (106 amino acids), and barnase (110 amino acids). These small proteins fold kinetically in an apparent two-state manner. However, we found that they have partially folded hidden intermediates after the rate-limiting transition states. Moreover, using a hydrogen exchange-directed protein engineering approach, we were able to populate the partially unfolded intermediate of Rd-apocyt b562 and determine its high-resolution structure. This is the first high-resolution structure of a folding intermediate. To our surprise, significant non-native hydrophobic interactions were found in the partially unfolded structure. These results contradict the so called "New View" of protein folding that hypothesizes that small proteins fold through multiple pathways without going through intermediate states but provide strong evidence for the earlier hypothesis that intermediates are important for solving the large-scale conformation search problem: the Levinthal paradox. We have also developed a theoretical model to explain why different small proteins (less than 120 amino acids) fold with different rates, which span six orders of magnitude from microseconds to seconds. We found that the size (number of folded residues) of the transition state is dominantly controlled by the topological complexity of the native structure and correlates with the folding rate. We also developed a theoretical model to explain why small proteins fold through intermediates.